This will be no different from creating any other new account, except that the existing MX records will need to be modified to make sure they point to an A record that points to the old server, and the A records for the site should point to your server.

MX records point to an A record, not an IP address, so you may need to make a new A record to which to point the MX records. For example, say you have the MX record mail.domain.com pointing to domain.com. If you change the A record for domain.com to point to your server, then when a mail server tries to send mail to doman.com, it is going to look up the MX record for domain.com, get mail.domain.com, and find that mail.domain.com points to domain.com - so mail will be delivered to your server.

To avoid this, change the A records for domain.com and www.domain.com to point to your server's IP address. Now, make a new A record, something like mail2.domain.com, and make the MX records point to that new A record. Make the A record mail2.domain.com point to the old server's IP address. That way, the old server will still handle mail, but your server will handle the site.